Arctangent Calculator

tan⁻¹(x) — find the angle whose tangent is x. Range (−90°, 90°).

Inputs

Result

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How to use this calculator

  • Enter any real number.
  • Read the angle.

About this calculator

arctan (tan⁻¹) returns the angle whose tangent is the input. Unlike arcsin/arccos, arctan accepts any real number as input. Principal range is (−90°, 90°), exclusive — never reaches the endpoints, only approaches them as |x| → ∞.

Frequently asked

Why does arctan have an open range?+
Because tan(90°) is undefined. arctan approaches 90° asymptotically as input → +∞.
What is atan2?+
A two-argument variant atan2(y, x) that returns angles in the full [−180°, 180°] range, accounting for quadrant. Standard in computer graphics.
Common values?+
arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°, arctan(∞) = 90° (limit only).
How is arctan used in slope problems?+
A line with slope m makes angle arctan(m) with the x-axis.
Does arctan work for negative inputs?+
Yes — arctan(−x) = −arctan(x). It's an odd function.

Related calculators

Tangent Calculator
tan(x) = sin(x) / cos(x). Undefined where cos(x) = 0 (at 90°, 270°, …).
Arcsine Calculator
sin⁻¹(x) — find the angle whose sine is x. Domain [-1, 1], range [−90°, 90°].
Arccosine Calculator
cos⁻¹(x) — find the angle whose cosine is x. Range [0°, 180°].
Sine Calculator
Compute sin(x) for any angle in degrees or radians.
Cosine Calculator
Compute cos(x) for any angle.
Slope Calculator
m = (y₂−y₁) / (x₂−x₁). Returns slope-intercept form y = mx + b.

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